Dimers

This will be a series of expository talks on the dimer model of a random surface. A dimer configuration on a graph is a set of edges of the graph (dimers) so that each vertex of the graph is an endpoint of exactly one edge in the set. For periodic planar graphs, the dimer configuration gives rise to a tessellation of the plane which in turn can be interpreted as a surface in three dimensions.

A probability measure on dimer configurations gives rise to random surfaces which model physical processes such as the melting of a crystal.

The primary goal of these talks will be to understanding the 2006 paper Dimers and Amoebae by R. Kenyon, A. Okounkov, and S. Sheffield, which exhibits a remarkable connection between the dimer model and algebraic curves.